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%I #27 Oct 11 2016 15:40:50
%S 0,1,1,1,1,1,2,1,2,1,2,1,2,2,1,1,1,2,3,1,2,2,3,1,2,2,3,2,3,1,2,1,2,1,
%T 2,2,3,3,2,1,2,2,3,2,2,3,4,1,3,2,1,2,3,3,2,2,3,3,4,1,2,2,3,1,2,2,3,1,
%U 3,2,3,2,3,3,2,3,2,2,3,1,4,2,3,2,1,3,3,2,3,2,3,3,2,4,3,1,2,3,2,2
%N Number of iterations of "take odd part of phi" (A053575) to reach 1 from n.
%C a(n) >= A256757(n) - 1.
%H T. D. Noe, <a href="/A227944/b227944.txt">Table of n, a(n) for n = 1..10000</a>
%F For n > 1, a(n) = a(A053575(n)) + 1.
%e a(18) = 2 because it takes two steps to reach 1 from 18: phi(18) = 6, the odd part of which is 3, and phi(3) = 2, the odd part of which is 1.
%e a(19) = 3 because it takes three steps to reach 1 from 19: phi(19) = 18, the odd part of which is 9, and phi(9) = 6, the odd part of which is 3, and phi(3) = 2, the odd part of which is 1.
%t oddPhi[n_] := Module[{phi = EulerPhi[n]}, phi/2^IntegerExponent[phi, 2]]; Table[Length[NestWhileList[oddPhi[#] &, n, # > 1 &]] - 1, {n, 100}] (* _T. D. Noe_, Oct 07 2013 *)
%o (Haskell)
%o a227944 n = fst $
%o until ((== 1) . snd) (\(i, x) -> (i + 1, a053575 x)) (0, n)
%o -- _Reinhard Zumkeller_, Oct 09 2013
%Y A variant of A049115: a(n) = A049115(n) unless n is a power of 2.
%Y Cf. A003434, A227946.
%K nonn,easy
%O 1,7
%A _Max Alekseyev_, Oct 03 2013
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